Problem: Dagogo uploads $3$ videos on his channel every month. Each video averages $15$ minutes in length and gets an average of $150{,}000$ new views. The average ratio of likes-to-views of Dagogo's videos is $1:5$. Dagogo wants to reach a total of $9{,}000{,}000$ views on his channel. Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?
Answer: There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say Dagogo gets $x\,\dfrac{\text{likes}}{\text{minute}}$. We are given that Dagogo gets $0.2\,\dfrac{\text{likes}}{\text{view}}$. How can we relate these two quantities with an equation? $\begin{aligned} 0.2\,\dfrac{\text{likes}}{\text{view}}\cdot y\,\dfrac{\text{views}}{\text{minute}}&=x\,\dfrac{\text{likes}}{\text{minute}} \end{aligned}$ So in order to find the rate $x$ of likes per minute, we need to figure out the value of $y$, which is the rate of views per minute of video. Notice what other information we are given: $3\,\dfrac{\text{videos}}{\text{month}}$ $15\,\dfrac{\text{minutes}}{\text{video}}$ $150{,}000\,\dfrac{\text{views}}{\text{video}}$ $9{,}000{,}000\,\text{views}$ Which of these quantities can help us calculate a rate whose units are $\dfrac{\text{views}}{\text{minute}}$ ? We can combine the following quantities: $\begin{aligned} &\phantom{=}\dfrac{150{,}000\,\dfrac{\text{views}}{\text{video}}}{15\,\dfrac{\text{minutes}}{\text{video}}} \\\\ &=\dfrac{150{,}000}{15}\,\dfrac{\text{views}}{\cancel\text{video}}\cdot\dfrac{\cancel\text{videos}}{\text{minute}} \\\\ &=10{,}000\,\dfrac{\text{views}}{\text{minute}} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} 0.2\,\dfrac{\text{likes}}{\text{view}}\cdot 10{,}000\,\dfrac{\text{views}}{\text{minute}}&=x\,\dfrac{\text{likes}}{\text{minute}} \\\\ 2000\,\dfrac{\text{likes}}{\text{minute}}&=x\,\dfrac{\text{likes}}{\text{minute}} \end{aligned}$ In conclusion, Dagogo gets, on average $2000$ likes for each minute of his videos.